Alternatively, you can try to get a private money loan or ask the seller to finance a portion to reduce the down payment, but typically equity is the preferred method when you need funds for a down payment.

If this is a short sale, I would recommend working with a broker who is experienced with short sales to handle this. 

It may be tough to do with inherited tenants because you weren't there when they moved in but this is a good way to handle it going forward

The problems you listed are fairly easy to fix and can be handled by a handy tenant. 

Yes, as long as your debt to income ratio could handle both.

Instead of rent credits, just reduce the sale price by the total amount of rent credit the tenant would have received. 

The big buyers that are larger companies handle everything in house once under contract but ultra high net worth individuals expect you to help them with everything along the way.    

I've never seen one where they reduce the price based on inspection.

Find a good RE attorney that can also handle the closing and escrow if you have it.

Additionally, my AC project needed some steam pipes moves, but because they were a plumbing and AC company, they were able to handle all of this (steam was too close to breaker boxes).If you have an older home you may have more electrical work needed than you think.